Electron Transitions

We saw in the last section that the energy of an atomic electron is proportional to the square of the ratio of two integers: the atomic number Z and the energy level n. This means that the energy is quantized: it can only have one of a discrete set of values. This is analogous to the situation we had with MRI, where the energy of the nuclear magnetic moment depended on the spin. Just as the nuclei could flip their spins with the absorption or emission of a photon of the correct energy, atomic electrons can change their energy levels via the same mechanism. If a photon has the same energy as the difference between two allowed energy levels, an electron at the lower level can absorb it and move to the higher level. If an electron moves to a lower level, it emits a photon with the correct frequency to conserve energy. When either of these things happen, we say that the electron has undergone a transition to another level. If an electron at energy level n absorbs a photon of energy -En, it is kicked out of the atom altogether. This means that -En is its ionization energy.

If we restrict ourselves to the naturally occurring elements, Z can be any integer from 1 (Hydrogen) to 92 (Uranium). When a given atom is in its ground state, all of its electrons are at their lowest possible energy level. The highest value of n for such an atom is 7 (in Uranium), but as we saw in the last section, an excited electron can have any value of n. Of course, as n approaches infinity, the energy differences between levels approaches zero, but there are still in any given atom a large number of significantly different energy levels. This means that there is a wide variety of photon energies which can cause transitions.

Photons associated with visible light have wavelengths in the range 700 (red) to 400 (blue) nm. Wavelengths above 700 are called infrared, and those below 400 are ultraviolet. Very high energy photons have wavelengths below 10 nm, and are called x-rays. All of these wavelengths are associated with atomic electron transitions, although it is not uncommon for the electrons in covalent bonds to absorb or emit photons in the visible and ultraviolet wavelengths.

(the vertical scale is relative intensity). Note that even though we speak of a single photon being scattered, the photon which is emitted is not the same photon that was absorbed: the absorbed photon no longer exists, its energy and angular momentum having been transferred to the absorbing electron.

Of course, an absorbed photon does not have to be re-emitted: its energy can be used for chemical purposes. Photosynthesis and sight are two prime examples. When a photon hits your retina, it is absorbed and the energy is used to start the process of image formation. Absorption of photons by chlorophyll results in the production of molecules used by the plant to store energy. And in the process of fluorescence, photons are absorbed and stored for a relatively long period of time before being re-emitted. During that time, we say the the electron is in a meta-stable state: it is not at its lowest energy, but its relaxation time is relatively long.